Geodesic
Abstract group actions of locally compact groups on CAT(0) spaces
Philip Möller1 ; Olga Varghese2
1University of Münster, Germany
2Otto-von-Guericke University Magdeburg, Germany
Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 863-887

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DOI

We study abstract group actions of locally compact Hausdorff groups on CAT(0) spaces. Under mild assumptions on the action we show that it is continuous or has a global fixed point. This mirrors results by Dudley and Morris–Nickolas for actions on trees. As a consequence we obtain a geometric proof for the fact that any abstract group homomorphism from a locally compact Hausdorff group into a torsion-free CAT(0) group is continuous.
DOI : 10.4171/ggd/677
Classification : 20-XX, 22-XX
Mots-clés : Automatic continuity, locally compact groups, CAT(0) spaces

Philip Möller  1   ; Olga Varghese  2

1 University of Münster, Germany
2 Otto-von-Guericke University Magdeburg, Germany 
Philip Möller; Olga Varghese. Abstract group actions of locally compact groups on CAT(0) spaces. Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 863-887. doi: 10.4171/ggd/677
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     title = {Abstract group actions of locally compact groups on {CAT(0)} spaces},
     journal = {Groups, geometry, and dynamics},
     pages = {863--887},
     year = {2022},
     volume = {16},
     number = {3},
     doi = {10.4171/ggd/677},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/677/}
}
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